Stability for a system of the 2D magnetohydrodynamic equations with partial dissipation

被引：12

作者：

Ji, Ruihong ^{[1
]}

Lin, Hongxia ^{[1
]}

Wu, Jiahong ^{[2
]}

Yan, Li ^{[1
]}

机构：

[1] Chengdu Univ Technol, Geomath Key Lab Sichuan Prov, Chengdu 610059, Sichuan, Peoples R China

[2] Oklahoma State Univ, Dept Math, Stillwater, OK 74078 USA

来源：

APPLIED MATHEMATICS LETTERS | 2019年 / 94卷

基金：

美国国家科学基金会; 中国博士后科学基金; 中国国家自然科学基金;

关键词：

Background magnetic field; Large-time behavior; Resistive magnetohydrodynamic equation; Stability; GLOBAL WELL-POSEDNESS; MHD EQUATIONS; EXISTENCE;

D O I：

10.1016/j.aml.2019.03.013

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper examines the stability problem on perturbations near a physically important steady state solution of the 2D magnetohydrodynamic (MHD) system with only partial dissipation. We obtain two main results. The first assesses the asymptotic linear stability with explicit decay rates while the second affirms the global stability in the Sobolev space H-1 setting. (C) 2019 Elsevier Ltd. All rights reserved.

引用

页码：244 / 249

页数：6

共 14 条

[1] Existence of electromagnetic-hydrodynamic waves [J].

Alfven, H .

NATURE, 1942, 150 :405-406

[2]

[Anonymous], 2014, ARXIV14045681V1MATHA

[3] LONGTIME DYNAMICS OF A CONDUCTIVE FLUID IN THE PRESENCE OF A STRONG MAGNETIC-FIELD [J].

BARDOS, C ;

SULEM, C ;

SULEM, PL .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1988, 305 (01) :175-191

[4] Global Well-Posedness of the Incompressible Magnetohydrodynamics [J].

Cai, Yuan ;

Lei, Zhen .

ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 2018, 228 (03) :969-993

[5] The 2D MHD equations with horizontal dissipation and horizontal magnetic diffusion [J].

Cao, Chongsheng ;

Regmi, Dipendra ;

Wu, Jiahong .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2013, 254 (07) :2661-2681

[6] Global regularity for the 2D MHD equations with mixed partial dissipation and magnetic diffusion [J].

Cao, Chongsheng ;

Wu, Jiahong .

ADVANCES IN MATHEMATICS, 2011, 226 (02) :1803-1822

[7]

He L., 2018, Ann. PDE, V4, pArt.5, DOI [10.1007/s40818-017-0041-9, DOI 10.1007/S40818-017-0041-9]

[8] The 2D magnetohydrodynamic equations with magnetic diffusion [J].

Jiu, Quansen ;

Niu, Dongjuan ;

Wu, Jiahong ;

Xu, Xiaojing ;

Yu, Huan .

NONLINEARITY, 2015, 28 (11) :3935-3955

[9]

Lin F., 2015, J DIFFER EQUATIONS, V259, P5440

[10] Global Classical Solutions of Three Dimensional Viscous MHD System Without Magnetic Diffusion on Periodic Boxes [J].

Pan, Ronghua ;

Zhou, Yi ;

Zhu, Yi .

ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 2018, 227 (02) :637-662

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